Pexeso

Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares so that they can make a pexeso. What dimension must squares have if their side is to be larger than 3cm and less than 10cm?

Correct answer:

x₁ =  60 mm
x₂ =  40 mm

Step-by-step explanation:

$$\begin{gathered} a=60\text{ cm}\to \text{ mm}=60\cdot 10\text{ mm}=600\text{ mm } \\ b=840\text{ mm } \\ 600=2^3\cdot 3\cdot 5^2 \\ 840=2^3\cdot 3\cdot 5\cdot 7 \\ \text{GCD}(600,840)=2^3\cdot 3\cdot 5=120 \\ y=GCD(a,b)=GCD(600,840)=120 \\ 30<x<100 \\ {x}_1=y\mathrm{/}2=120\mathrm{/}2=60\text{ mm} \end{gathered}$$

$x_2=y\mathrm{/}3=120\mathrm{/}3=40\text{ mm}$

Try another example

Related math problems and questions:

• Cutting paper
  Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square.
• Paper squares
  The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
• Plumber
  The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?
• Square tiles
  The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor.
• Pegs
  From two sticks 240 cm and 210 cm long, it is necessary to cut the longest possible pegs for flowers so that no residues remain. How many pegs will it be?
• Gardens colony
  Gardens colony with dimensions of 180 m and 300 m are to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
• Glass panel
  A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
• Two rulers
  We have two rulers. Scale interval on first rulers are a spaced 1 cm and on second spaced 15 mm. Rulers are attached to each other so that they match initial divider commas. What next dividers commas coincide? Find at least three cases.
• Cubes
  Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.
• On Children's
  On Children's Day, the organizers bought 252 chewing gums, 396 candies and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way.
• Garden
  The garden has the shape of a rectangle measuring 19m²⁰cm and 21m60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent p
• School books
  At the beginning of the school year, the teacher distributed 480 workbooks and 220 textbooks. How many pupils could have the most in the classroom?
• Groups
  In the 6th class there are 60 girls and 72 boys. We want to divide them into groups so that the number of girls and boys is the same. How many groups can you create? How many girls will be in the group?
• The classroom
  The classroom is 9 meters long. The width of the classroom is smaller and can be passed in equally long steps of 55 CM or 70 CM. Determine the width of the classroom.
• Plums
  In the bowl are plums. How many would be there if we can divide it equally among 8, 10 and 11 children?
• Tiles
  Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled, and how many we need them?
• Steps
  Peter makes steps long 70 cm, John 45 cm long. After how many meters their footsteps meet?